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There are three different ways that two lines can interact.
I. Intersecting Lines

Intersection
Intersecting lines are lines that meet.
There are two important factors with two intersecting lines:

A) Two lines will intersect in a single point. This point is a point of each line.

B) There's no way to construct two straight lines and have them intersect in more than one point.

II. Parallel Lines
Parallel lines are lines that never meet. A set of parallel lines always travels in the same direction.
Parallel Lines
Parallel lines always stay equal distance from each other.

II. Skew Lines
Skew lines do not intersect, but they do not travel in the same direction.
Skew lines cannot exist in two dimensions.

The figure below is turning on the 'y axis' to give you a better look at two skew lines.
The skew lines are the blue and green lines. The black lines are the axes.
Notice how they do not intersect but are not parallel.
Skew Lines

For a stereographic (or 3D) representation of skew lines, click here.

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